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A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

1
Office of School Enterprise Cooperation and Innovation and Entrepreneurship Education, Shaanxi Vocational and Technical College, Xi’an 710038, China
2
Department of Mathematics, The University of Poonch Rawalakot, Azad Kashmir 10250, Pakistan
3
Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan
4
Abdus Salam School of Mathematical Sciences, Lahore 54000, Pakistan
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School of information Engineering, Xi’an University, Xi’an 710065, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 536; https://doi.org/10.3390/math8040536
Received: 26 February 2020 / Revised: 25 March 2020 / Accepted: 29 March 2020 / Published: 4 April 2020
The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations. View Full-Text
Keywords: host-parasitoid model; stability analysis; Neimark-Sacker bifurcation; chaos control host-parasitoid model; stability analysis; Neimark-Sacker bifurcation; chaos control
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MDPI and ACS Style

Ma, X.; Din, Q.; Rafaqat, M.; Javaid, N.; Feng, Y. A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control. Mathematics 2020, 8, 536.

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